# Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)

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Poster Fast Bayesian Optimal Experimental Design for Seismic Source Inversion

(2016-01-06) Long, Quan; Motamed, Mohammad; Tempone, Raul; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; United Technologies Research Center; University of New MexicoWe develop a fast method for optimally designing experiments [1] in the context of statistical seismic source inversion [2]. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by the elastic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the true parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.

Poster Optimized Energy Efficiency and Spectral Efficiency Resource Allocation Strategies for Phantom Cellular Networks

(2016-01-06) Abdelhady, Amr Mohamed Abdelaziz; Amin, Osama; Alouini, Mohamed-Slim; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering ProgramMulti-teir hetrogeneous networks have become an essential constituent for next generation cellular networks. Meanwhile, energy efficiency (EE) has been considered a critical design criterion along with the traditional spectral efficiency (SE) metric. In this context, we study power and spectrum allocation for the recently proposed two-teir architecture known as Phantom cellular networks. The optimization framework includes both EE and SE, where we propose an algorithm that computes the SE and EE resource allocation for Phantom cellular networks. Then, we compare the performance of both design strategies versus the number of users, and the ration of Phantom cellresource blocks to the total number or resource blocks. We aim to investigate the effect of some system parameters to acheive improved SE or EE performance at a non-significant loss in EE or SE performance, respectively. It was found that the system parameters can be tuned so that the EE solution does not yield a significant loss in the SE performance.

Poster A multilevel adaptive reaction-splitting method for SRNs

(2016-01-06) Moraes, Alvaro; Tempone, Raul; Vilanova, Pedro; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionIn [5], we present a novel multilevel Monte Carlo method for kinetic simulation of stochastic reaction networks (SRNs) specifically designed for systems in which the set of reaction channels can be adaptively partitioned into two subsets characterized by either high or low activity. To estimate expected values of observables of the system, our method bounds the global computational error to be below a prescribed tolerance, TOL, within a given confidence level. This is achieved with a computational complexity of order O(TOL-2). We also present a novel control variate technique which may dramatically reduce the variance of the coarsest level at a negligible computational cost.

Poster Hybrid Chernoff Tau-Leap

(2016-01-06) Moraes, Alvaro; Tempone, Raul; Vilanova, Pedro; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionMarkovian pure jump processes can model many phenomena, e.g. chemical reactions at molecular level, protein transcription and translation, spread of epidemics diseases in small populations and in wireless communication networks among many others. In this work we present a novel hybrid algorithm for simulating individual trajectories which adaptively switches between the SSA and the Chernoff tauleap methods. This allows us to: (a) control the global exit probability of any simulated trajectory, (b) obtain accurate and computable estimates for the expected value of any smooth observable of the process with minimal computational work.

Poster Performance Analysis of Communications under Energy Harvesting Constraints with noisy CSI

(2016-01-06) Znaidi, Mohamed Ridha; Rezki, Zouheir; Tembine, Hamidou; Alouini, Mohamed-Slim; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering Program; NYU Abu DhabiIn energy harvesting communications, the transmitters have to adapt transmission to availability of energy harvested during the course of communication. The performance of the transmission depends on the channel conditions which vary randomly due to environmental changes. In this work, we consider the problem of power allocation taking into account the energy arrivals over time and the degree of channel state information (CSI) available at the transmitter, to maximize the throughput. Differently from previous work, the CSI at the transmitter is not perfect and may include estimation errors. We solve this problem with respect to the Energy Harvesting constraints. We determine the optimal power in the case where the channel is assumed to be perfectly known at the receiver. Also, we obtain the power policy when the transmitter has no CSI. Furthermore, we analyze the asymptotic average throughput in a system where the average recharge rate goes asymptotically to zero and when it is very high.